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Solutions of the Bethe ansatz equations associated to the XXX model of asimple Lie algebra come in families called the populations. We prove that apopulation is isomorphic to the flag variety of the Langlands dual Lie algebra.The proof is based on the correspondence between the solutions of the Betheansatz equations and special difference operators which we call the discreteMiura opers. The notion of a discrete Miura oper is one of the main results ofthe paper.  For a discrete Miura oper D, associated to a point of a population, we showthat all solutions of the difference equation DY=0 are rational functions, andthe solutions can be written explicitly in terms of points composing thepopulation.Comment: Latex, 26 page

Discrete Miura Opers and Solutions of the Bethe Ansatz Equations